A stock has had returns of 11 percent, 18 percent, 20 percent, −13 percent, 25 percent, and −9 percent over the last six years.

A stock has had returns of 11 percent, 18 percent, 20 percent, −13 percent, 25 percent, and −9 percent over the last six years.
What are the arithmetic and geometric average returns for the stock?

Explanation

The arithmetic average return is the sum of the known returns divided by the number of returns, so:

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Suppose a stock had an initial price of $84 per share, paid a dividend of $1.50 per share during the year, and had an ending share price of $92.

Compute the percentage total return, dividend yield, and capital gains yield.
Suppose a stock had an initial price of $84 per share, paid a dividend of $1.50 per share during the year, and had an ending share price of $92.
What was the dividend yield and the capital gains yield?

Explanation
The dividend yield is the dividend divided by the beginning of the period price, so:


Dividend yield = $1.50/$84
Dividend yield = .0179, or 1.79%


And the capital gains yield is the increase in price divided by the initial price, so:


Capital gains yield = ($92 – 84)/$84
Capital gains yield = .0952, or 9.52%

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Problem 12-7 Calculating Returns and Variability [LO1]

Problem 12-7 Calculating Returns and Variability [LO1]

	Returns
Year	X			Y
1		12	%		18	%
2		26			27
3		12			10
4	–	19		–	24
5		10			18

  

Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Explanation The average return is the sum of the returns, divided by the number of returns. The average return for each stock was:

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You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 14 percent, –14 percent, 16 percent, 26 percent, and 10 percent. Suppose the average inflation rate over this period was 3.5 percent and the average T-bill rate over the period was 4 percent.

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 14 percent, –14 percent, 16 percent, 26 percent, and 10 percent. Suppose the average inflation rate over this period was 3.5 percent and the average T-bill rate over the period was 4 percent.



a.
What was the average real return on the company’s stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b. What was the average nominal risk premium on the company’s stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.)

Explanation

a.

To find the average return, we sum all the returns and divide by the number of returns, so:

Average return = (.14 – .14 + .16 + .26 + .10)/5

Average return = .104, or 10.4%

To calculate the average real return, we can use the average return of the asset, and the average inflation rate in the Fisher equation. Doing so, we find:

(1 + R) = (1 + r)(1 + h)

= (1.104/1.035) – 1

= .0667, or 6.67%

b.

The average risk premium is the average return of the asset, minus the average risk-free rate, so, the average risk premium for this asset would be:

Average risk premium = Average return − Average risk-free rate

Average risk premium = .104 − .040

Average risk premium = .064, or 6.4%

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Suppose a stock had an initial price of $90 per share, paid a dividend of $2.40 per share during the year, and had an ending share price of $76.

Suppose a stock had an initial price of $90 per share, paid a dividend of $2.40 per share during the year, and had an ending share price of $76.

Compute the percentage total return, dividend yield, and capital gains yield.

Explanation

Using the equation for total return, we find:

R = ($76 – 90 + 2.40)/$90

R = −.1289, or −12.89%

And the dividend yield and capital gains yield are:

Dividend yield = $2.40/$90

Dividend yield = .0267, or 2.67%

Capital gains yield = ($76 – 90)/$90

Capital gains yield = −.1556, or −15.56%

Here’s a question for you: Can the dividend yield ever be negative? No, that would mean you were paying the company for the privilege of owning the stock. It has happened on bonds.

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